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If a Graph G is Eulerian then all nodes will have Even degree But is the reverse True i.e. for any graph G’ if nodes of G’ have even degrees then G’ is Eulerian?
in Mathematical Logic 13 points 11 views
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Yes. 

If a simple graph G is connected and the degree of every vertex of G is a positive even integer, then G has an Euler circuit.

https://math.berkeley.edu/~arash/55/10_5.pdf

https://courses.engr.illinois.edu/cs173/su2014/Lectures/Euler.pdf

 

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